Advance Example

Rob has bundle of pages 5110. Would he able to distribute them with 4 clients
equally?

He would not able to distribute 5110 pages with 4 clients equally.

Explanation :

In the number 5110, the number formed by the digits in the tens and unit places
is 10.
The number 10 is not divisible by 4 so that, the number 5110 is not divisible by
4.

Tests for divisibility by 5

If a number has either 0 or 5 in its units place, then that number is divisible
by 5.

Simple Example

let’s say the number 3035.
The number 3035 has 5 in its unit place. So that 3035 is divisible by 5.

Tests for divisibility by 6

If a number can be divided by the numbers 2 as well as 3, then that number is divisible
by 6.

Simple Example

1. let’s say the number 55128
The number 55128 has 8 in the unit place. There it is divisible by 2. The sum of
the digits in the number 55128 is 5+ 5+1+2+8= 21 . 21 is divisible by 3. Therefore,
55128 is divisible by 6.

2. let’s say the number 45120.
The number 45120 has 0 in the unit place. There it is divisible by 2. The sum of
the digits in the number 45120 is 4+5+1+3+0= 13. 13 is not divisible by 3. Therefore,
45120 is not divisible by 6.

Tests for divisibility by 9

If the sum of the digits in a number is divisible by 9, then that number is divisible
by 9.

Simple Example

let’s say the number 55008.
The sum of the digits in the number 55008 is 5+5+0+0+8= 18. 18 is divisible by
9. Therefore, 55008 is divisible by 9.

Medium Example:

let’s say the number 2247.
The sum of the digits in the number 2247 is 2+2+4+7= 15. 15 is not divisible by
9. Therefore, 2247 is not divisible by 9.

Tests for divisibility by 10

If a number has 0 in its units place, then that number is divisible by 10.

Simple Example

let’s say the number 3050.
The number 3050 has 0 in its unit place. So that 3050 is divisible by 10.

Tests for divisibility by 11

If the difference between the sums obtained by adding alternate digits of the number
is 0 or is divisible by 11 then that number is also divisible by 11.

Simple Example

let’s say the number 1463.
The sums of the alternate digits of the number 1463 are 1+6= 7 and 4+3= 7. the
difference between them is 7-7= 0. Therefore, 1463 is also divisible by 11.

Medium Example:

let’s say the number 8243
The sums of the alternate digits of the number 8243 are 8+4= 12 and 2+3= 5. The
difference between them is 12-5= 7. 7 is not divisible by 11.Therefore, 8243 is
not divisible by 11.

Divisors of number.

The quotients obtained by dividing the number are the Divisors of number. To find divisor of 15, divide 15 by 3. We get 5 as quotients. So that, 3 and 5 is the divisor of 15.

Medium Example:

Divisors of 420 are 1, 2, 3, 5, 10, 42, 70, 84, 140, 210, 420

Explanation:

We will use tests of divisibility here.420 is divisible by 2. 420/2 = 210.420 is divisible by 10. 420/10 = 42.420 is divisible by 5. 420 /5 = 84.420 is divisible by 3. 420 /3 = 140420 is divisible by 2 and 3. So that, 420 is divisible by 6.
420
/6 = 70.Now every number is divisible by number 1 and itself

Advance Example:

Divisors of 8965 are 1, 5, 11, 815, 1993,8965

Explanation:

We will use tests of divisibility here.
You can see that 8965 has 5 in its unit place. Hence, 8965 is divisible
by 5. 8965/5 = 1993.
The sums of the alternate digits of the number 8965 are 8+6= 14 and 9+5= 14.
The difference between them is 14-14= 0. Therefore, 8965 is also divisible
by 11. 8965/11= 8158965 is divisible by number 1 and itself.